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A241220 Number of lines through at least two points of a centered hexagonal grid of size n. 2
0, 15, 84, 312, 852, 1878, 3654, 6546, 10680, 16668, 25002, 35910, 50136, 68190, 90462, 118200, 152274, 192828, 240480, 296880, 361962, 437832, 525756, 625440, 739146, 867864, 1011822, 1174062, 1354572, 1554114, 1775568, 2020848, 2289054, 2582760, 2905410 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Hex Number.

PROG

(PARI)

c(n, s, fmin, fmax)={sum(k=1+s, n, max(0, fmax(k-s)-max(fmin(k)-1, if(k-2*s>0, fmax(k-2*s)))))}

b(n, u, v)={c(2*n-1, u, i->max(0, i-n)+1+i\u*v, i->min(i, n)+n-1+i\u*v)}

a(n)={3*((n>1)*(2*n-1) + sum(u=1, 2*n-3, sum(v=1, 2*n-2-u, if(gcd(u, v)==1, b(n, u, v), 0))))} \\ Andrew Howroyd, Sep 18 2017

CROSSREFS

Cf. A018808, A241219, A003215.

Sequence in context: A247958 A108674 A050405 * A279740 A281189 A206383

Adjacent sequences:  A241217 A241218 A241219 * A241221 A241222 A241223

KEYWORD

nonn

AUTHOR

Martin Renner, Apr 17 2014

EXTENSIONS

a(15)-a(16) from Martin Renner, Apr 27 2014

Terms a(17) and beyond from Andrew Howroyd, Sep 18 2017

STATUS

approved

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Last modified February 21 14:40 EST 2018. Contains 299414 sequences. (Running on oeis4.)